pyqint 0.6.0

Python package for evaluating integrals of Gaussian type orbitals in electronic structure calculations

PyQInt

Table of Contents

• Purpose
• Installation
  • Anaconda
  • PyPi
• Usage
  • Overlap integrals
  • Kinetic integrals
  • Nuclear attraction integrals
  • Two-electron integrals
  • Construction of Contracted Gaussian Functions
  • Quick evaluation of integrals

Purpose

PyQInt is a Python package for calculating one- and two-electron integrals as encountered in electronic structure calculations. Since integral evaluation can be quite computationally intensive, they are programmed in C++ and connected to Python using Cython.

Installation

Anaconda

Open Anaconda prompt and type

conda install -c ifilot pyqint

PyPi

Open a terminal and type

pip install pyqint

Usage

Overlap integrals

from pyqint import PyQInt, cgf, gto
import numpy as np
from copy import deepcopy

# construct integrator object
integrator = PyQInt()

# build cgf for hydrogen separated by 1.4 a.u.
cgf1 = cgf([0.0, 0.0, 0.0])

cgf1.add_gto(0.154329, 3.425251, 0, 0, 0)
cgf1.add_gto(0.535328, 0.623914, 0, 0, 0)
cgf1.add_gto(0.444635, 0.168855, 0, 0, 0)

# create a copy of the CGF
cgf2 = deepcopy(cgf1)
cgf2.p[2] = 1.4

# construct empty matrix
S = np.zeros((2,2))
S[0,0] = integrator.overlap(cgf1, cgf1)
S[0,1] = S[1,0] = integrator.overlap(cgf1, cgf2)
S[1,1] = integrator.overlap(cgf2, cgf2)

# output result
print(S)

Kinetic integrals

from pyqint import PyQInt, cgf, gto
import numpy as np
from copy import deepcopy

# construct integrator object
integrator = PyQInt()

# build cgf for hydrogen separated by 1.4 a.u.
cgf1 = cgf([0.0, 0.0, 0.0])

cgf1.add_gto(0.154329, 3.425251, 0, 0, 0)
cgf1.add_gto(0.535328, 0.623914, 0, 0, 0)
cgf1.add_gto(0.444635, 0.168855, 0, 0, 0)

# create a copy of the CGF
cgf2 = deepcopy(cgf1)
cgf2.p[2] = 1.4

# construct empty matrix
T = np.zeros((2,2))
T[0,0] = integrator.kinetic(cgf1, cgf1)
T[0,1] = T[1,0] = integrator.kinetic(cgf1, cgf2)
T[1,1] = integrator.kinetic(cgf2, cgf2)

# output result
print(T)

Nuclear attraction integrals

from pyqint import PyQInt, cgf, gto
import numpy as np
from copy import deepcopy

# construct integrator object
integrator = PyQInt()

# build cgf for hydrogen separated by 1.4 a.u.
cgf1 = cgf([0.0, 0.0, 0.0])

cgf1.add_gto(0.154329, 3.425251, 0, 0, 0)
cgf1.add_gto(0.535328, 0.623914, 0, 0, 0)
cgf1.add_gto(0.444635, 0.168855, 0, 0, 0)

# create a copy of the CGF
cgf2 = deepcopy(cgf1)
cgf2.p[2] = 1.4

# Build nuclear attraction integrals
V1 = np.zeros((2,2))
V1[0,0] = integrator.nuclear(cgf1, cgf1, cgf1.p, 1)
V1[0,1] = V1[1,0] = integrator.nuclear(cgf1, cgf2, cgf1.p, 1)
V1[1,1] = integrator.nuclear(cgf2, cgf2, cgf1.p, 1)

V2 = np.zeros((2,2))
V2[0,0] = integrator.nuclear(cgf1, cgf1, cgf2.p, 1)
V2[0,1] = V2[1,0] = integrator.nuclear(cgf1, cgf2, cgf2.p, 1)
V2[1,1] = integrator.nuclear(cgf2, cgf2, cgf2.p, 1)

# print result
print(V1,V2)

Two-electron integrals

from pyqint import PyQInt, cgf, gto
import numpy as np
from copy import deepcopy

# construct integrator object
integrator = PyQInt()

# build cgf for hydrogen separated by 1.4 a.u.
cgf1 = cgf([0.0, 0.0, 0.0])

cgf1.add_gto(0.154329, 3.425251, 0, 0, 0)
cgf1.add_gto(0.535328, 0.623914, 0, 0, 0)
cgf1.add_gto(0.444635, 0.168855, 0, 0, 0)

# create a copy of the CGF
cgf2 = deepcopy(cgf1)
cgf2.p[2] = 1.4

T1111 = integrator.repulsion(cgf1, cgf1, cgf1, cgf1)
T1122 = integrator.repulsion(cgf1, cgf1, cgf2, cgf2)
T1112 = integrator.repulsion(cgf1, cgf1, cgf1, cgf2)
T2121 = integrator.repulsion(cgf2, cgf1, cgf2, cgf1)
T1222 = integrator.repulsion(cgf1, cgf2, cgf2, cgf2)
T2211 = integrator.repulsion(cgf2, cgf2, cgf1, cgf1)

print(T1111)
print(T1122)
print(T1112)
print(T2121)
print(T1222)
print(T2211)

Construction of Contracted Gaussian Functions

from pyqint import PyQInt, Molecule
import numpy as np

# construct integrator object
integrator = PyQInt()

# build hydrogen molecule
mol = Molecule()
mol.add_atom('H', 0.0, 0.0, 0.0)
mol.add_atom('H', 0.0, 0.0, 1.4)
cgfs, nuclei = mol.build_basis('sto3g')

print(cgfs, nuclei)

Parallel evaluation of integrals

From a collection of Contracted Gaussian Functions, the complete set of overlap, kinetic, nuclear attraction and two-electron integrals can be quickly evaluated using the build_integrals function. Using the npar argument, the number of threads to be spawned can be set.

from pyqint import PyQInt, Molecule
import numpy as np

# construct integrator object
integrator = PyQInt()

# build hydrogen molecule
mol = Molecule()
mol.add_atom('H', 0.0, 0.0, 0.0)
mol.add_atom('H', 0.0, 0.0, 1.4)
cgfs, nuclei = mol.build_basis('sto3g')

# evaluate all integrals
ncpu = multiprocessing.cpu_count()
S, T, V, teint = integrator.build_integrals(cgfs, nuclei, npar=ncpu, verbose=False)

print(S, T, V, teint)